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Black_prince [1.1K]
3 years ago
15

Find all the zeros of the function g(x)=x^3-4x^2-x+22

Mathematics
1 answer:
vagabundo [1.1K]3 years ago
5 0

Answer:

x = -2, x = 3 − i√8, and x = 3 + i√8

Step-by-step explanation:

g(x) = x³ − 4x² − x + 22

This is a cubic equation, so it must have either 1 or 3 real roots.

Using rational root theorem, we can check if any of those real roots are rational.  Possible rational roots are ±1, ±2, ±11, and ±22.

g(-1) = 18

g(1) = 18

g(-2) = 0

g(2) = 12

g(-11) = 1782

g(11) = 858

g(-22) = -12540

g(22) = 8712

We know -2 is a root.  The other two roots are irrational.  To find them, we must find the other factor of g(x).  We can do this using long division, or we can factor using grouping.

g(x) = x³ − 4x² − 12x + 11x + 22

g(x) = x (x² − 4x − 12) + 11 (x + 2)

g(x) = x (x − 6) (x + 2) + 11 (x + 2)

g(x) = (x (x − 6) + 11) (x + 2)

g(x) = (x² − 6x + 11) (x + 2)

x² − 6x + 11 = 0

Quadratic formula:

x = [ 6 ± √(36 − 4(1)(11)) ] / 2

x = (6 ± 2i√8) / 2

x = 3 ± i√8

The three roots are x = -2, x = 3 − i√8, and x = 3 + i√8.

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WINSTONCH [101]

\frac{1}{4}  -  \frac{ - 3}{8}  =  \frac{5}{8}
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Find the missing length for the right triangle described below. B = 21 ft, c=27 ft. Find side a. Round to the nearest whole numb
maksim [4K]

Answer:

16.97 ft

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Side B = 21 ft

Side c = 27 ft

As we know, formula for right triangle is as follows,

a^{2} + b^{2} = c^{2}

a^{2} = c^{2} - b^{2}

So, by putting the value in the formula, we get,

a^{2} = 27^{2} - 21^{2}

a^{2} = 729 - 441

a^{2} = 288

a = 16.97 ft

Hence, the length of the side  for the right triangle is 16.97ft.

6 0
3 years ago
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nexus9112 [7]
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3 years ago
Simplify (b^4)^3. ❤️ SLAT*_^}
KiRa [710]

Answer:

b^1^2

Step-by-step explanation:

<em>First, multiply by exponent rule.</em>

<em>(x^y)^z=x^y^z</em>

<em>b^4^*^3</em>

<em>Then, multiply by the numbers from left to right.</em>

<em>4*3=12</em>

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